Geodesic
Hilbert's Nullstellensatz in algebraic geometry over rigid soluble groups
Izvestiya. Mathematics , Tome 79 (2015) no. 5, pp. 1051-1063.

Voir la notice de l'article provenant de la source Math-Net.Ru

We discuss the problem of the possible form of an analogue of the classical Nullstellensatz of Hilbert in algebraic geometry over a suitable class of groups and prove such an analogue in the class of rigid soluble groups.
Keywords: algebraic geometry.
Mots-clés : group, soluble group 
@article{IM2_2015_79_5_a7,
     author = {N. S. Romanovskiy},
     title = {Hilbert's {Nullstellensatz} in algebraic geometry over rigid soluble groups},
     journal = {Izvestiya. Mathematics },
     pages = {1051--1063},
     publisher = {mathdoc},
     volume = {79},
     number = {5},
     year = {2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2015_79_5_a7/}
}
TY  - JOUR
AU  - N. S. Romanovskiy
TI  - Hilbert's Nullstellensatz in algebraic geometry over rigid soluble groups
JO  - Izvestiya. Mathematics 
PY  - 2015
SP  - 1051
EP  - 1063
VL  - 79
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_2015_79_5_a7/
LA  - en
ID  - IM2_2015_79_5_a7
ER  - 
%0 Journal Article
%A N. S. Romanovskiy
%T Hilbert's Nullstellensatz in algebraic geometry over rigid soluble groups
%J Izvestiya. Mathematics 
%D 2015
%P 1051-1063
%V 79
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_2015_79_5_a7/
%G en
%F IM2_2015_79_5_a7
N. S. Romanovskiy. Hilbert's Nullstellensatz in algebraic geometry over rigid soluble groups. Izvestiya. Mathematics , Tome 79 (2015) no. 5, pp. 1051-1063. http://geodesic.mathdoc.fr/item/IM2_2015_79_5_a7/

[1] G. Baumslag, A. Myasnikov, V. Remeslennikov, “Algebraic geometry over groups. I. Algebraic sets and ideal theory”, J. Algebra, 219:1 (1999), 16–79 | DOI | MR | Zbl

[2] A. Myasnikov, V. Remeslennikov, “Algebraic geometry over groups. II. Logical foundations”, J. Algebra, 234:1 (2000), 225–276 | DOI | MR | Zbl

[3] W. R. Scott, “Algebraically closed groups”, Proc. Amer. Math. Soc., 2:1 (1951), 118–121 | DOI | MR | Zbl

[4] N. S. Romanovskii, “Equational Noetherianness of rigid soluble groups”, Algebra Logic, 48:2 (2009), 147–160 | DOI | MR | Zbl

[5] N. S. Romanovskii, “Divisible rigid groups”, Algebra Logic, 47:6 (2008), 426–434 | DOI | MR | Zbl

[6] A. G. Myasnikov, N. S. Romanovskii, “Logical aspects of the theory of divisible rigid groups”, Dokl. Math., 90:3 (2014), 697–698 | DOI | Zbl

[7] N. S. Romanovskii, “Irreducible algebraic sets over divisible decomposed rigid groups”, Algebra Logic, 48:6 (2009), 449–464 | DOI | MR | Zbl

[8] A. Myasnikov, N. Romanovskiy, “Krull dimension of solvable groups”, J. Algebra, 324:10 (2010), 2814–2831 | DOI | MR | Zbl